I have both of UA's original models of running shoes. By far, they have the most support of any running shoes I have. They have a unique band that wraps around your arch and gives great support as you tighten your shoe. Hard to explain but I don't know of any other shoes that have this feature.

The tread doesn't look particularly aggressive... I've done steep trails in regular running shoes before and it's fine. But I do prefer trail runners as they feel a lot more grippy, especially on rock.